Although we started this study from a different perspective than HOFM [1]}, our feature interaction method is equivalent to the alternative recursion form of HOFM.
Therefore, HOFM can be viewed as a special case of HONAM.
Suppose that each feature network is linear, and the output weight is an all-one matrix.
HONAM is equivalent to HOFM.
Furthermore, HONAM overcomes the limitations of the existing FM/HOFM, feature interaction methods, and NAM.
First, vanilla HOFM in the original work [2]} has the time complexity of \(O(km^t)\) , but our feature interactions method has the time complexity of \(O(tkm)\)  when using dynamic programming as mentioned above; where \(k\)  is the embedding size.
Second, since FM/HOFM and other feature interaction methods are essentially linear models, their expressive powers are limited. HONAM can learn non-linear functions and has high expressive power because it utilizes neural networks, and is still interpretable.
Third, NAM can only model 1st-order feature interactions, whereas HONAM can model high-order feature interactions. Thus, HONAM has higher predictive performance than NAM and can provide high-quality interpretations.
